A Shell oil rig that was adrift in the Gulf of Alaska has been brought under control, the company reported Monday.

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An enormous Shell Oil offshore rig that had broken free and gone adrift in stormy seas in the Gulf of Alaska for the better part of three days was brought under control Monday, the company said.

“The situation is stabilizing,” said Curtis Smith, a spokesman for Shell in Anchorage.

Two tow lines from the rig, the Kulluk, which was used for test drilling in the Arctic last summer, had been reattached to support ships about 19 miles south of Kodiak Island, and officials were discussing what to do next.

“We feel considerably more positive about the situation,” Smith said.

The Kulluk, one of two rigs that Shell used to drill test wells off the North Slope of Alaska as part of the company’s ambitious and expensive effort to open Arctic waters to oil production, was being towed to a Seattle shipyard for offseason maintenance when the line to its towing vessel, the Aiviq, separated during a storm Thursday. The Aiviq then lost power, and other support ships and a Coast Guard cutter were brought in to help with engine repairs and to reconnect tow lines to the Kulluk, which does not have its own propulsion system.

The 18 workers aboard the rig were evacuated by Coast Guard helicopters Saturday.

Support crews struggled in 25-foot swells to reconnect tow lines, succeeding several times. But each time the lines separated again, leaving the rig, 266 feet in diameter, in danger of drifting toward land.

A Coast Guard spokesman, Petty Officer 1st Class David Mosley, said the seas began to calm late Sunday. A tow line from the Kulluk was connected to a tug shortly after midnight, and the rig was reconnected to the Aiviq, its power restored, at 5 a.m. Monday.

Smith said a unified command, with representatives from the Coast Guard, the state, Shell and a contractor, was evaluating its options. One possibility would be to take the Kulluk into a protected harbor until the weather clears in a few days.

The Kulluk, which was built in Japan in 1983 and upgraded over the past six years at a cost of $292 million, is designed for icy conditions in the Arctic. It was at Vigor Shipyards in Seattle, being refurbished, for about a year before it was taken north. It can drill in up to 400 feet of water and up to 20,000 feet deep. During drilling season it carries a crew of about 140 people, Smith said.

Shell has spent six years and more than $4 billion in its effort to drill in Arctic waters, one of the last untapped oil-producing regions in the United States. But the effort has faced regulatory hurdles and opposition from Native-American and environmental groups.

Last summer, the Kulluk drilled a shallow test well in the Beaufort Sea while another rig drilled a similar hole in the Chukchi Sea to the west. But Shell announced in September that it would be forced to delay further drilling until next year after a specialized piece of equipment designed to contain oil from a spill was damaged in a testing accident.

The episode was one of a number of setbacks for the Arctic drilling program this year. Shell says it hopes to drill five exploratory wells in the region during the 2013 drilling season, which begins in mid-July.